Finite Group Databasebeta

← #27195676

Subgroups — #27195676

Order 13184.

362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268358C211yesmaximal, characteristic
2#20267809C212yesmaximal, complemented
3C2×#15692938C211yesmaximal, characteristic, complemented
4#20267547C212yesmaximal, complemented
5#518×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C2211yescharacteristic
7C2×#13110089C2212yes—
8#15693017C412yescomplemented
9#15693008C412yescomplemented
10#15692992—22no—
11#15692990—22no—
12#15692980C2211yescharacteristic
13#15692949—24no—
14#15692938—22no—
15C22×D4×C103C2211yescharacteristic
16C4×D4×C103—24no—
17#117×C103C2212yes—
18C2×C22⋊C4×C103—22no—
19#13110105—22no—
20#13110105—22no—
21C2×Dic206C2×C411yescharacteristic, complemented
22C2×D412C2×C411yescharacteristic, complemented
23C2×C22⋊D103—21no—
24C2×C22⋊D103—24no—
25C2×C4×D103—21no—
26#13110089—22no—
27#13110089—22no—
28C2×C103⋊C8—22no—
29C4⋊Dic103—21no—
30C22⋊Dic103—24no—
31C22⋊Dic103—21no—
32C4×Dic103C2×C412yescomplemented
33C24×C103D412yes—
34C2×D4×C103—22no—
35C2×D4×C103—22no—
36C2×D4×C103C2×C412yes—
37C2×D4×C103D412yes—
38C22×C4×C103—24no—
39C22×C4×C103C2311yescharacteristic
40C4⋊C4×C103—22no—
41C22⋊C4×C103—24no—
42C22⋊C4×C103—22no—
43C42×C103D414yescomplemented
44C23×C103—22no—
45C23×C103—22no—
46C23×C103—82no—
47C23×C103C22⋊C414yes—
48C23×C103C2×D411yescharacteristic
49C22×D103—21no—
50D4×C103—24no—
51D4×C103—24no—
52C2×C4×C103—24no—
53C2×C4×C103—84no—
54C2×C4×C103C22×C411yescharacteristic
55C2×C4×C103C2×D412yes—
56C2×C4×C103C2×D411yescharacteristic
57C2×C4×C103#4112yes—
58C22⋊D103—41no—
59C22⋊D103—41no—
60C22⋊D103—84no—
61C2×Dic103—22no—
62C2×Dic103—21no—
63D412—22no—
64C4×D103—42no—
65Dic206—22no—
66C103⋊C8—42no—
67C22×C103—24no—
68C22×C103—41no—
69C22×C103—44no—
70C22×C103—44no—
71C22×C103—82no—
72C22×C103C2×C22⋊C411yescharacteristic
73C22×C103#12011yescharacteristic
74C22×C103#12311yescharacteristic
75C2×D103—42no—
76C2×D103—41no—
77C4×C103—44no—
78C4×C103C4×D412yes—
79C4×C103#12112yes—
80Dic103—42no—
81Dic103—41no—
82C2×C103—21no—
83C2×C103—21no—
84C2×C103—21no—
85C2×C103—44no—
86C2×C103#38611yescharacteristic
87D103—81no—
88#1911—1031nomaximal, Sylow
89C103#191111yescharacteristic, complemented, Sylow
90#535—1031no—
91#518D10311yescharacteristic, complemented
92#421—1032no—
93C2×#100—1031no—
94H(3,ℤ/4)—1032no—
95C2×#41—1031no—
96C22×D4C2×D10311yescharacteristic
97C2×M16—1032no—
98#127—1032no—
99#124—1032no—
100#121—2062no—
101#120—2062no—
102C4×D4—24no—
103#117—1031no—
104#117C2×D10312yes—
105C2×C22⋊C4—22no—
106#104—2064no—
107#100—2062no—
108C24C22⋊D10312yes—
109#41—2062no—
110#41—2062no—
111C2×Q8—1031no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—1031no—
115C2×D4—2064no—
116C2×D4—2061no—
117C2×D4C4×D10312yes—
118C2×D4D41212yes—
119C22×C4—24no—
120C22×C4—2061no—
121C22×C4C22×D10311yescharacteristic
122M16—2062no—
123M16—2062no—
124C2×C8—2062no—
125C4⋊C4—22no—
126C4⋊C4—2061no—
127C22⋊C4—24no—
128C22⋊C4—22no—
129C22⋊C4—2064no—
130C22⋊C4—2061no—
131C42—1032no—
132C42C22⋊D10314yescomplemented
133C23—22no—
134C23—22no—
135C23—82no—
136C23—2061no—
137C23(C2×D103)⋊C414yes—
138C23C2×C22⋊D10311yescharacteristic
139Q8—2062no—
140D4—24no—
141D4—24no—
142D4—8244no—
143D4—4121no—
144D4—4121no—
145D4—2062no—
146C2×C4—24no—
147C2×C4—84no—
148C2×C4—4122no—
149C2×C4—2062no—
150C2×C4—2061no—
151C2×C4C2×C4×D10311yescharacteristic
152C2×C4C2×C22⋊D10312yes—
153C2×C4C2×D41211yescharacteristic
154C2×C4#1311010512yes—
155C8—4122no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—4122no—
162C22—4121no—
163C22C2×(C2×D103)⋊C411yescharacteristic
164C22#1569299011yescharacteristic
165C22#1569300411yescharacteristic
166C4—44no—
167C4—4122no—
168C4—4121no—
169C4C4×C22⋊D10312yes—
170C4#1569299512yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—8241no—
176C2#2026767011yescharacteristic
subgroupG/H
centerC2#20267670
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#518×C103C2
socleC2×C103#386
prime radical#20268358C2
cosocleC22×C4×C103C23
hypercenter#518D103
hypocenterC103#1911
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #20267809C2semidirect
3. C2×#15692938C2semidirect
4. #20267547C2semidirect
5. #518×C103C2semidirect
8. #15693017C4semidirect
9. #15693008C4semidirect
21. C2×Dic206C2×C4semidirect
22. C2×D412C2×C4semidirect
32. C4×Dic103C2×C4semidirect
43. C42×C103D4semidirect
89. C103#1911semidirect
91. #518D103semidirect
132. C42C22⋊D103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202683582
#202678092
C2×#156929382
#202675472
#518×C1032
#1911103